Geometry - Final Exam Review

Transcription

1 Geometry - Final Exam Review Write your answers and show all work on these pages. This review is printed on both sides of the paper and has 28 questions, and it will be checked daily and graded! 1. Part A: Reflect ΔABC over the x-axis and list the new coordinates. Part B: Translate ΔA B C from Part A RIGHT 5 units and DOWN 1 unit and list the new coordinates. Part C: Rotate ΔA B C 180 o about the x-axis and list the new coordinates.

2 2. Triangle ABC is shown in the coordinate plane below. Draw the result of the transformation when triangle ABC is translated 8 units to the right, down 2 units and then rotated 90 o clockwise about the origin. Show all your work. Part A: Translate 8 units to the right, down 2 units. List the new coordinates Part B: Rotate 90 o clockwise about the origin. List the new coordinates

3 3. Triangle BCD and triangle XYZ are shown in the coordinate plane below. Explain the transformation or sequence of transformations of triangle BCD to triangle XYZ using one or more translations, reflections, and rotations.

4 4. Find the measure of each angle and its relationship to the angle indicated. 1 = 128 o 2 = because it is with 1 3 = because it is with 2 4 = because it is with 3 5 = because it is with 4 6 = because it is with 5 7 = because it is with 6 8 = because it is with 7 9 = because it is with 8 10 = because it is with 9 11 = because it is with = because it is with = because it is with = because it is with = because it is with = because it is with = because it is with Line l is parallel to line m. Find the measure of each angle and its relationship to the angle indicated. m 1 = 65 2= because it is with given 3= because it is with 2 4= because it is with 3 5= because it is with 4 6= because it is with 5 7= because it is with 6 8= because it is with 7

5 6. Find the value of the variables. Show your work x y w v 65 0 z 7. Find the values of the variables.

6 8. ΔABC is dilated by a scale factor of 2 to form ΔA B C. Identify if the following statements are TRUE or FALSE. A A B B AA A B AA CC = 2 1 AA A B = BB B C

7 9. Given that A B C is the image of ΔABC under a dilation with scale factor 1 3 and center at point O, decide which statements must be true. For all of the false statements, alter the statement so that it is true. Statement A A Must be True? Corrections (if needed) Statement AA BB = A C B C Must be True? Corrections (if needed) B C CC C B AA IIA B AA A C = BB B C AA CC = 1 3 AA A C AA A B = 1 3

8 10. D G C F E H The measures of two of the three angles in a triangle are given. Part A: Find the measures of the missing angles in each triangle. Part B: Are the two triangles similar? If so write a similarity statement and why they are similar? 11. Determine if the triangles below are similar. If so, tell why and write the similarity statement. Similar? Why? Similarity Statement:

9 12. In each pair of triangles determine if they are congruent by SSS, SAS, ASA, AAS or not congruent. PICTURE SSS, SAS, ASA, AAS or NOT CONGRUENT

10 13.

11 14. To find the height of a lamppost at a park, Jade placed a mirror on the ground 10 feet from the base of the lamppost. She then stepped back 2 feet so that she could see the top of the lamp post in the center of the mirror. Jade's eyes are 5 feet 4 inches above the ground. What is the height, in feet, of the lamppost? Jade 15. Find the height of the tree.

12 16. The map shows a straight highway between Amusement Park and the Lake. Highway planners want to build a new gas station equidistant between the two locations. Find the coordinates of the new gas station. 17.

13 18. A 12-foot ladder is placed against the side of a building as shown in Figure 1 below. The bottom of the ladder is 6 feet from the base of the building. In order to increase the reach of the ladder against the building, the ladder is moved 2 feet closer to the base of the building as shown in Figure ft 12 ft 6 ft To the nearest foot, how much farther up the building does the ladder now reach? Show how you arrived at your answer. 19. You are walking around the pond in the local park. How much shorter is the distance across the pond than around it?

14 20. Write the Trigonometric Ratios of C and B. Part A: sin B = cos B = sin C = cos C = Part B: Find the measures of B and C choosing one of the ratios above. Round to the nearest degree. tan B = tan C = 21. Using the given triangle, write the trig ratios in fraction and decimal form. Sin R = Sin S = Cos R = Cos S = Tan R = Tan S = Find the measures of R and S choosing one of the ratios above. Round to the nearest degree.

15 Find the following values based on Circle A C Find x B Find BC 76 x A 64 Find y Find B y 24 E D Find DE Find EC z Find CD Find BBB Find C

16 24. In the diagram FE and FFF are tangent to ʘ. Find the measure of each indicated arc, or angle

17 25. Fill in the chart with the appropriate information. (-2, 2) 2 (x 3) 2 + (y + 5) 2 = 25

18 26. In the coordinate plane, quadrilateral ABCD has vertices with coordinates 3, 4, 5, 4, 5, 3, D 3, 3. A ( ) B ( ) C ( ) and ( ) Part A: Compute the lengths of the sides of quadrilateral ABCD. Round to the nearest tenth. AB = BC = CD = DA = Perimeter of quadrilateral ABCD= Part B: Compute the slopes of the sides AB and AD. Slope of A A = Slope of CCC = Slope of AA= Slope of BBB = Part C: Indicate in the table below whether ABCD is an example of each shape listed. Explain why it is or is not.

19 27. You just placed two scoops of delicious ice cream on a sugar cone. As you are about to take the first bite, your mom asks if the ice cream can all fit inside the cone. The ice cream cone has a radius of 4 cm and a height of 15 cm. If the scoop of ice cream is a sphere with radius of 4.5 cm, will all of the ice cream fit inside the cone? If not how much more ice cream is there? 28. Twelve cans are being packed into a cardboard box for shipping. The cans are arranged in four rows of three and fit snugly into the box. Each can is 6 inches tall and has a three inch diameter. How much empty space will there be left in the box after all the cans are packed? Clearly show and label all your calculations.